464 CHEMICAL ENGINEERING The general methods for measuring resistance include the Wheatstone bridge, the Thomson bridge, potentiometer, and differential galvanometer. The Wheatstone bridge is used the most extensively for industrial installations. Three-lead Wheatstone Bridge Method.—Figure 27 illustrates the wiring diagram for a simple Wheatstone bridge and thermometer with the Siemens three-lead compensation. The platinum or gold lead wires C'd and T'e in the thermometer are constructed of as nearly the same resistance as possible, and the copper lead wires CC' and TT' must also have an equivalent resistance. The battery B is connected between the ratio arms TI and r<i of the bridge and to the compensating lead wire cd. A sensitive FIG. 27.—Three-lead Wheatstone bridge. FIG. 28.—Four-lead Wheatstone. galvanometer G is connected to the points / and g as illustrated. By varying the setting of the dial or slide wire 7-3 the bridge is balanced until the galvanometer shows zero deflection. Whence from the principle of the balanced Wheatstone bridge we obtain the following relation. r3 + Cd = rH-JTf 7*1 r2 If TI is constructed equal to r2) since Cd = Te, the setting of the slide wire or dial n gives directly the value of the resistance of the coil, i.e. r3 = r4. Hence, the measured resistance is independent of the resistance of the lead wires. For industrial use the slide wire of the bridge is graduated directly in degrees of temperature. Figure 28 illustrates the wiring diagram for a simple Wheatstone bridge and thermometer of the four-lead potential terminal type. This method is used mainly for precision measurements in the laboratory. The battery B is first connected to c. As before, when the bridge is balanced we obtain : rz + Cd = 7-4-1- Te The battery is then connected to the terminal t and the terminals T and C are interchanged. We accordingly have for a balance: r'3 4. Te = r 4 + Cd. Whence upon combining these two equations: Thus the measured resistance of the coil is independent of the resistance of the lead wires and any error which would result from inequality of the lead resistances Cd and Te in the ordinary three-lead thermometer is eliminated.